MN15-L: A New Local Exchange-Correlation Functional for Kohn–Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids

Abstract

Kohn-Sham density functional theory is widely used for applications of electronic structure theory in chemistry, materials science, and condensed-matter physics, but the accuracy depends on the quality of the exchange-correlation functional. Here, we present a new local exchange-correlation functional called MN15-L that predicts accurate results for a broad range of molecular and solid-state properties including main-group bond energies, transition metal bond energies, reaction barrier heights, noncovalent interactions, atomic excitation energies, ionization potentials, electron affinities, total atomic energies, hydrocarbon thermochemistry, and lattice constants of solids. The MN15-L functional has the same mathematical form as a previous meta-nonseparable gradient approximation exchange-correlation functional, MN12-L, but it is improved because we optimized it against a larger database, designated 2015A, and included smoothness restraints; the optimization has a much better representation of transition metals. The mean unsigned error on 422 chemical energies is 2.32 kcal/mol, which is the best among all tested functionals, with or without nonlocal exchange. The MN15-L functional also provides good results for test sets that are outside the training set. A key issue is that the functional is local (no nonlocal exchange or nonlocal correlation), which makes it relatively economical for treating large and complex systems and solids. Another key advantage is that medium-range correlation energy is built in so that one does not need to add damped dispersion by molecular mechanics in order to predict accurate noncovalent binding energies. We believe that the MN15-L functional should be useful for a wide variety of applications in chemistry, physics, materials science, and molecular biology.

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…[26] and the SSCE8 results in Ref. [35]. Concerning the (less investigated) bulk moduli, Figure 9b shows that the relative performances of functionals are preserved, also because bulk moduli show small variations among functionals.…”

“…The function in Equation 35 is limited in the range [-1/b,1] and it is a monotonic decreasing function: in the isoorbital regions (a KS % 0) f % 1, in the slowly varying density regions (a KS % 1) f % 0, and in the multi-orbital regions (a KS ) 1) f % 2ð1=bÞ.…”

“…The final B97M2V functional form contains 4 BSparameters for exchange and eight for correlation, and fulfills the HEG limit. For the exchange we have: NGA-Local (MN15-L) K-meta-NGA functionals [34,35] have both the general expression…”

“…(2) The recent class of KED dependent meta-nonseparable gradient approximation (K-meta-NGA), [34,35] which also use s KS and rq (but not r 2 q). The NGA is based on the work of Liu and Parr.…”

“…Many K-meta-GGAs have been developed, both empirical and nonempirical. One important feature of K-meta-GGAs is that they can be made one-electron self-correlation-free.(2) The recent class of KED dependent meta-nonseparable gradient approximation (K-meta-NGA), [34,35] which also use s KS and rq (but not r 2 q). The NGA is based on the work of Liu and Parr.…”